Proof of the triviality of ·d4 field theory and some mean-field features of Ising models for d>4

Michael Aizenman

doi:10.1103/PhysRevLett.47.1

Proof of the triviality of ·d4 field theory and some mean-field features of Ising models for d>4

Michael Aizenman

Research output: Contribution to journal › Article › peer-review

290 Scopus citations

Abstract

It is rigorously proved that the continuum limits of Euclidean ·d4 lattice fields are free fields in d>4. An exact geometric characterization of criticality in Ising models is introduced, and used to prove other mean-field features for d>4 and hyperscaling in d=2.

Original language	English (US)
Pages (from-to)	1-4
Number of pages	4
Journal	Physical review letters
Volume	47
Issue number	1
DOIs	https://doi.org/10.1103/PhysRevLett.47.1
State	Published - 1981

All Science Journal Classification (ASJC) codes

General Physics and Astronomy

Access to Document

10.1103/PhysRevLett.47.1

Cite this

@article{fb26c5cdbbd64ee1934ce8dc9eb4a27f,

title = "Proof of the triviality of ·d4 field theory and some mean-field features of Ising models for d>4",

abstract = "It is rigorously proved that the continuum limits of Euclidean ·d4 lattice fields are free fields in d>4. An exact geometric characterization of criticality in Ising models is introduced, and used to prove other mean-field features for d>4 and hyperscaling in d=2.",

author = "Michael Aizenman",

year = "1981",

doi = "10.1103/PhysRevLett.47.1",

language = "English (US)",

volume = "47",

pages = "1--4",

journal = "Physical review letters",

issn = "0031-9007",

publisher = "American Physical Society",

number = "1",

}

TY - JOUR

T1 - Proof of the triviality of ·d4 field theory and some mean-field features of Ising models for d>4

AU - Aizenman, Michael

PY - 1981

Y1 - 1981

N2 - It is rigorously proved that the continuum limits of Euclidean ·d4 lattice fields are free fields in d>4. An exact geometric characterization of criticality in Ising models is introduced, and used to prove other mean-field features for d>4 and hyperscaling in d=2.

AB - It is rigorously proved that the continuum limits of Euclidean ·d4 lattice fields are free fields in d>4. An exact geometric characterization of criticality in Ising models is introduced, and used to prove other mean-field features for d>4 and hyperscaling in d=2.

UR - http://www.scopus.com/inward/record.url?scp=24444435550&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=24444435550&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.47.1

DO - 10.1103/PhysRevLett.47.1

M3 - Article

AN - SCOPUS:24444435550

SN - 0031-9007

VL - 47

SP - 1

EP - 4

JO - Physical review letters

JF - Physical review letters

IS - 1

ER -

Proof of the triviality of ·d4 field theory and some mean-field features of Ising models for d>4

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this